Prepare the Baking Dishes: Preheat oven to 350°F. Generously butter 2 (14-ounce) or 4 (8-ounce) ramekins, ensuring every surface is well-coated to prevent sticking. The proper preparation of your ramekins is crucial for easy removal of the puddings later.
Create the Date Mixture: Combine chopped dates and baking soda in a heat-proof bowl. Pour hot milk over the mixture and let sit for 10 minutes to soften the dates and allow the baking soda to activate. After soaking, blend the mixture into a smooth paste using an immersion blender or regular blender.
Make the Chocolate Base: In a separate bowl, whisk cocoa powder with hot water until it forms a smooth paste. Beat in the soft butter, brown sugar, and vanilla extract until well combined. Add the date paste followed by the whole egg and egg yolk, mixing thoroughly after each addition to create a rich, smooth batter.
Incorporate Dry Ingredients: In another bowl, mix flour, baking powder, espresso powder (if using), and salt. Gently fold this dry mixture into the wet ingredients until smooth and no flour pockets remain. Take care not to overmix, which could make your puddings tough.
Bake the Puddings: Divide the batter evenly between the prepared ramekins. Bake for 28-33 minutes for 8-ounce ramekins or 35-40 minutes for 14-ounce ramekins until the centers are just firm to the touch but still slightly moist. The puddings should spring back when lightly pressed.
Prepare the Chocolate Sauce: While the puddings are baking, combine all sauce ingredients in a saucepan over medium heat. Cook, stirring frequently, until the chocolate and butter have melted and the sauce is smooth and slightly thickened. Keep warm until ready to use.
Finish and Serve: While the puddings are still warm, poke several holes in the top of each with a skewer or toothpick. Pour about half of the warm chocolate sauce over the puddings and allow it to soak in for a few minutes. Carefully invert the puddings onto serving plates. Serve with a scoop of vanilla ice cream and drizzle with the remaining chocolate sauce.